Unconditional convergence of conservative spectral Galerkin methods for the coupled fractional nonlinear Klein-Gordon-Schrödinger equations

DOI10.1007/s10915-023-02108-6arXiv2210.02101OpenAlexW4319601642MaRDI QIDQ6158992

Yu Shun Wang, Yayun Fu, Wenjun Cai, Dongdong Hu

Publication date: 20 June 2023

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2210.02101

zbMATH Keywords

convergencespectral Galerkin methodunique solvabilitystructure-preserving algorithmRiesz fractional derivative

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Fractional derivatives and integrals (26A33) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Fractional partial differential equations (35R11) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (3)

On convergence of a novel linear conservative scheme for the two-dimensional fractional nonlinear Schrödinger equation with wave operator ⋮ Energy dissipation-preserving GSAV-Fourier-Galerkin spectral schemes for space-fractional nonlinear wave equations in multiple dimensions ⋮ Fully decoupled, linear, and energy-preserving GSAV difference schemes for the nonlocal coupled sine-Gordon equations in multiple dimensions

Cites Work

• Unnamed Item
• Blowup for fractional NLS
• An energy conservative difference scheme for the nonlinear fractional Schrödinger equations
• Hitchhiker's guide to the fractional Sobolev spaces
• Nonlinear fractional Schrödinger equations in one dimension
• A second order finite difference-spectral method for space fractional diffusion equations
• A uniformly accurate (UA) multiscale time integrator Fourier pseudospectral method for the Klein-Gordon-Schrödinger equations in the nonrelativistic limit regime, A UA method for Klein-Gordon-schrodinger equation
• Fractional Gagliardo-Nirenberg and Hardy inequalities under Lorentz norms
• Local structure-preserving algorithms for partial differential equations
• Fractional quantum mechanics and Lévy path integrals
• The scalar auxiliary variable (SAV) approach for gradient flows
• On the continuum limit for discrete NLS with long-range lattice interactions
• Efficient energy preserving Galerkin-Legendre spectral methods for fractional nonlinear Schrödinger equation with wave operator
• Fast conservative numerical algorithm for the coupled fractional Klein-Gordon-Schrödinger equation
• Structure-preserving algorithms for the two-dimensional fractional Klein-Gordon-Schrödinger equation
• On the propagation of regularity for solutions of the fractional Korteweg-de Vries equation
• A fourth-order dissipation-preserving algorithm with fast implementation for space fractional nonlinear damped wave equations
• A finite volume method for two-dimensional Riemann-Liouville space-fractional diffusion equation and its efficient implementation
• Efficient structure preserving schemes for the Klein-Gordon-Schrödinger equations
• Existence of solutions of an explicit energy-conserving scheme for a fractional Klein-Gordon-Zakharov system
• Efficient linear schemes with unconditional energy stability for the phase field elastic bending energy model
• Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian
• Line Integral Methods for Conservative Problems
• Spectral Methods
• Symplectic Geometric Algorithms for Hamiltonian Systems
• Attractors for the Klein–Gordon–Schrödinger equation
• Analysis and Approximation of a Fractional Cahn--Hilliard Equation
• A conservative spectral Galerkin method for the coupled nonlinear space-fractional Schrödinger equations
• The Exponential Scalar Auxiliary Variable (E-SAV) Approach for Phase Field Models and Its Explicit Computing
• A New Energy-Preserving Scheme for the Fractional Klein-Gordon-Schrodinger Equations
• An Efficient Spectral Petrov-Galerkin Method for Nonlinear Hamiltonian Systems
• Mass- and Energy-Conserved Numerical Schemes for Nonlinear Schr ¨odinger Equations
• A Fourth-order Compact ADI scheme for Two-Dimensional Nonlinear Space Fractional Schrödinger Equation
• Finite time blowup for Klein‐Gordon‐Schrödinger system
• A Crank--Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation
• A new class of energy-preserving numerical integration methods
• Geometric Numerical Integration
• Global attractors for the Klein-Gordon-Schrödinger equation in unbounded domains

This page was built for publication: Unconditional convergence of conservative spectral Galerkin methods for the coupled fractional nonlinear Klein-Gordon-Schrödinger equations